Braid group action and quasi-split affine $ı$quantum groups II: higher rank

Abstract

This paper studies quantum symmetric pairs $(\tilde{\mathbf{U}},{\tilde{\mathbf{U}}}^{ı})$ associated with quasi-split Satake diagrams of affine type $A_{2r-1},D_r,E_6$ with a nontrivial diagram involution fixing the affine simple node. Various real and imaginary root vectors for the universal $ı$quantum groups ${\tilde{\mathbf{U}}}^{ı}$ are constructed with the help of the relative braid group action, and they are used to construct affine rank one subalgebras of ${\tilde{\mathbf{U}}}^{ı}$. We then establish relations among real and imaginary root vectors in different affine rank one subalgebras and use them to give a Drinfeld type presentation of ${\tilde{\mathbf{U}}}^{ı}$.

V2, 32 pages, some edits and corrections, updated references, to appear in CMP